NAG Library Manual, Mark 28.4
```    Program f08tafe

!     F08TAF Example Program Text

!     Mark 28.4 Release. NAG Copyright 2022.

!     .. Use Statements ..
Use nag_library, Only: dspgv, dtpcon, f06rdf, nag_wp, x02ajf
!     .. Implicit None Statement ..
Implicit None
!     .. Parameters ..
Integer, Parameter               :: nin = 5, nout = 6
Character (1), Parameter         :: uplo = 'U'
!     .. Local Scalars ..
Real (Kind=nag_wp)               :: anorm, bnorm, eps, rcond, rcondb,    &
t1, t2
Integer                          :: i, info, j, n
!     .. Local Arrays ..
Real (Kind=nag_wp), Allocatable  :: ap(:), bp(:), eerbnd(:), w(:),       &
work(:)
Real (Kind=nag_wp)               :: dummy(1,1)
Integer, Allocatable             :: iwork(:)
!     .. Intrinsic Procedures ..
Intrinsic                        :: abs
!     .. Executable Statements ..
Write (nout,*) 'F08TAF Example Program Results'
Write (nout,*)
!     Skip heading in data file

Allocate (ap((n*(n+1))/2),bp((n*(n+1))/2),eerbnd(n),w(n),work(3*n),iwork &
(n))

!     Read the upper or lower triangular parts of the matrices A and
!     B from data file

If (uplo=='U') Then
Else If (uplo=='L') Then
End If

!     Compute the one-norms of the symmetric matrices A and B

anorm = f06rdf('One norm',uplo,n,ap,work)
bnorm = f06rdf('One norm',uplo,n,bp,work)

!     Solve the generalized symmetric eigenvalue problem
!     A*x = lambda*B*x (itype = 1)

!     The NAG name equivalent of dspgv is f08taf
Call dspgv(1,'No vectors',uplo,n,ap,bp,w,dummy,1,work,info)

If (info==0) Then

!       Print solution

Write (nout,*) 'Eigenvalues'
Write (nout,99999) w(1:n)

!       Call DTPCON (F07UGF) to estimate the reciprocal condition
!       number of the Cholesky factor of B.  Note that:
!       cond(B) = 1/rcond**2

Call dtpcon('One norm',uplo,'Non-unit',n,bp,rcond,work,iwork,info)

!       Print the reciprocal condition number of B

rcondb = rcond**2
Write (nout,*)
Write (nout,*) 'Estimate of reciprocal condition number for B'
Write (nout,99998) rcondb

!       Get the machine precision, eps, and if rcondb is not less
!       than eps**2, compute error estimates for the eigenvalues

eps = x02ajf()
If (rcond>=eps) Then
t1 = eps/rcondb
t2 = anorm/bnorm
Do i = 1, n
eerbnd(i) = t1*(t2+abs(w(i)))
End Do

!         Print the approximate error bounds for the eigenvalues

Write (nout,*)
Write (nout,*) 'Error estimates for the eigenvalues'
Write (nout,99998) eerbnd(1:n)
Else
Write (nout,*)
Write (nout,*) 'B is very ill-conditioned, error ',                  &
'estimates have not been computed'
End If
Else If (info>n .And. info<=2*n) Then
i = info - n
Write (nout,99997) 'The leading minor of order ', i,                   &
' of B is not positive definite'
Else
Write (nout,99996) 'Failure in DSPGV. INFO =', info
End If

99999 Format (3X,(6F11.4))
99998 Format (4X,1P,6E11.1)
99997 Format (1X,A,I4,A)
99996 Format (1X,A,I4)
End Program f08tafe
```